The National Gallery plans to mount one of the most ambitious exhibitions of paintings by Leonardo da Vinci ever undertaken, it announced today.

Given that there are arguably only 14 surviving Leonardo panel paintings anywhere in the world, it is clearly a difficult show to put on. But inspired by the recent restoration of the gallery's Leonardo painting, The Virgin of the Rocks, the gallery hopes to gather at least four more to create the most complete exhibition of the artist's surviving paintings ever held.

Luke Syson, the gallery's curator of Italian paintings before 1500, said the whole project was "very ambitious but thrilling", not least because there are so few paintings. "Leonardo essentially believed that it was better to have a tiny body of work of extraordinary quality rather than just churning stuff out."

The show will focus on Leonardo's years at the court of Milan in the late 1480s and 1490s – so not the Mona Lisa period, not that the Louvre would ever lend it.

The London exhibition will take place in the winter of 2011-12 and, so far, it has loan agreements for La Belle Fèrroniere, above, from the Louvre, the Madonna Litta, from the Hermitage and Saint Jerome from the Vatican. Syson said great effort had been put into persuading galleries of the scholarly benefits of seeing Leonardo's work together.

The gallery's other big show of 2011 will be the first exhibition in 40 years to be devoted to Flemish artist Jan Gossaert, one of the superstars of the northern Renaissance known particularly for his sensuous nudes and Dutch burghers. It will take place between 23 February and 30 May.

The free exhibitions in 2011 will include a collection of 19th century Norwegian and Swiss landscapes; a display of pre-1500 Italian altarpieces to be shown in the Sainsbury wing; and a show about the National Gallery's first director, Sir Charles Eastlake. Before all those there will be a show paying tribute to a living artist, Bridget Riley, which opens on 24 November this year.